La La Land,” in theory, is a movie that needs no explanation. The simplest thing you could call it is “an old-fashioned musical” — which means, of course, that it’s a big colorful splashy cornball swoon of a movie, one that traffics in the kind of billboard emotions (Love! Sadness! Joy!) and timeless Hollywood forms (Singing! Dancing! A Lavish Freeway Production Number Done In One Unbroken Take!) that can hit audiences like a sweet shot to the heart. That’s the beauty of it, right?

Yet “La La Land” isn’t just old-fashioned. It’s the new-fangled version of a sprawling Tinseltown classic. It’s Old Hollywood meets Jacques Demy meets “New York, New York” meets postmodern indie backlot passion. It’s a grand Los Angeles epic that features “mainstream” sentiments, but it’s also a subtle and idiosyncratic journey that’s almost entirely unpredictable. (Half an hour before it ends, you’ll have no idea where it’s going.) It’s Boy Meets Girl meets the precarious freedom of 21st-century love. It truly is a romance, but it’s also about what it takes to be an artist in a world that may or may not believe in art anymore.

I liked “La La Land” a lot the first time I saw it, but I confess that I didn’t fall head over tap shoes in love with it until I’d seen it a second time. That’s just the way it happens with certain movies; even a great one can kick in more fully on the second date. Here are a few thoughts as to why Damien Chazelle’s film, for all the spangly seduction of its surface, is a movie whose very rapture is elusive and off-center. (Once you’ve hooked into it, though, the rapture seems more heightened because of its off-centeredness.) “La La Land” isn’t just a stylized nostalgia trip of champagne montages and harmonizing hearts. It’s a filmmaking trifecta — it hooks the heart, the eye, and the mind. And once it snags you, it keeps getting better. Here’s why — though please know that I can’t talk about “La La Land” without revealing crucial aspects of it, so if you’re looking to see the movie unspoiled, don’t read on.

There’s a challenge built into the film’s structure. Okay, so you’re sitting there watching “La La Land.” You’ve seen Mia (Emma Stone), a plucky but desperate barista-slash-actress (that hidden underlayer of anxiety is where the potency of Stone’s performance begins), and Sebastian (Ryan Gosling), a retro-obsessive jazz pianist with a real snob edge to him, meet and square off, bicker like alley cats, do a soft-shoe against the magic-hour L.A. carpet of urban lights, and sing a song (in that same sequence) about how they don’t like each other — which, of course, is the moment they start to like each other. Finally, they go on a date to see “Rebel Without a Cause,” which ends with the two of them heading from the Rialto Theater to Griffith Observatory, where they enter the planetarium and are lofted, in the headiness of their romance, right up to the stars.

That moment is the climax of an intoxicating journey into the sweetness of old-movie love, and it ends with an iris shot right out of a silent film: the image closing down into a tiny circle against the darkness. You’re about an hour into the film — and what you don’t realize, yet, is that that’s the fading moment of its confectionary studio-system daydream aesthetic. From here on in, no more nifty choreographed numbers. No more dancing on air. The glorious sprawling freeway jam that opens the movie? You won’t see another sequence like it. This is all by design, but to go with the flow of “La La Land,” you have to drift for a long time, in the second half, into a very different mood: downbeat, contemporary, a place where production numbers — with their promise of instant mood enhancement — have gone away. You have to realize that you’re now watching…

…a Jacques Demy movie. And here’s what that means. To make “La La Land,” Chazelle drew — in form and spirit — on two celebrated French musicals directed by Jacques Demy in the ’60s: “The Umbrellas of Cherbourg” (1964) and “The Young Girls of Rochefort” (1967). There’s a lot you could say about those films — one thing I’ll say right up front is that I’ve never actually been wild about either of them — but they have a doleful wistful quality that’s strikingly and soulfully European. “Umbrellas” is the better of them, and the more radical achievement: Every line of it is sung, but it’s a pop operetta of the everyday, with lyrics that sound like conversation (a lot of them don’t rhyme), and it tells a story that throws you for a loop: It’s about a girl (Catherine Deneuve) who works in her mother’s umbrella shop, the mechanic (Nino Castelnuovo) she’s in love with, and what happens when he goes off to join the military. The two pledge their love to each other, but then…it fades. Why? Lots of reasons, but the real reason is that love, in “The Umbrellas of Cherbourg,” is a delicate and nearly arbitrary thing, a bit like the weather. (The film opens with a summer rain and ends with a cold snow.)

I’ve always had two essential feelings about “The Umbrellas of Cherbourg.” One is that it has the single most haunting theme song in the history of motion pictures (and I really mean that). The opening sequence, which consists of nothing more than an aerial view of a bunch of people walking under umbrellas accompanied by…that song, can reduce me to a blubbering baby in about 45 seconds. The music, by Michel Legrand, is grand. And so, believe it or not, is the wallpaper. (Most dazzling wallpaper in a movie. Ever.) But the story, as it unfolds, is…strange. Nearly philosophical in the frosty abstraction of its melancholy. The final scene is two people who were once in love running into each other for the first time in many years, and neither of them bats an eye. Which is supposed to demonstrate something. I confess, though: I’ve never gotten it. And I don’t buy it.

But I buy “La La Land,” which takes what’s great about the Jacques Demy musicals — the formal daring, the sweet sadness, the willingness to portray love as a highly imperfect thing — and restores the faith that Demy replaced with a forlorn shrug. “The Young Girls of Rochefort” is probably a more direct stylistic influence on “La La Land”: crowds of people in ordinary dress erupting into song and dance along a roadway, a fusion of MGM and new-wave naturalism. Yet what Chazelle ultimately got from Demy was a feeling, a lush open-endedness: the idea that the ultimate stylized romantic movie form — the musical — could contain a love story about people who drift apart as much as they come together. It’s the same life-goes-on notion that Woody Allen played with in “Annie Hall,” and in “La La Land” Chazelle does it full justice. As much as Jacques Demy (no, I’ll say it: better than Jacques Demy), he made a poetic fantasia about the way old-fashioned love fits into the new-fashioned world. Of course, it helps that he has a co-creator who provided…

The greatest original songs ever composed for a contemporary movie musical. Just think about “Singin’ in the Rain.” There are so many things that make it (arguably) the most sublime big-screen musical of all time, but take away the title song, and you don’t have the full magic. Even the quintessential image of Gene Kelly sashaying through puddles comes at us through those indelible musical notes. The melodies that Justin Hurwitz composed for “La La Land” have that rare kind of luscious defining earworm tastiness, and not to take away from Damien Chazelle’s wizardry, but if the songs weren’t that good, the movie wouldn’t be either.

Everyone will have his or her favorite. The one that’s currently being pushed for the Oscars, “City of Stars,” is my third or fourth favorite. It’s an exquisitely mournful yet seductive number (and the image of Ryan Gosling, with his ordinary-guy croon, singing it to two middle-aged strangers on the Hermosa Beach Pier is one of the film’s most memorable), but I actually prefer the electric infectiousness of the film’s opening mambo, “Another Day of Sun,” which played in my head for three months after I first heard it, and the great “Audition (The Fools Who Dream),” the song sung by Emma Stone in which the film’s emotions of love and loss fuse into its theme: that those who live to create are flaky, difficult, moonstruck, maybe somewhat mad beings who cause distress through their passion — yet the world needs them like oxygen. The song comes at the end of the lengthy detour “La La Land” takes away from singing-and-dancing exuberance, and that’s part of what makes it a deliverance. We’re back in old-musical Heaven! When Emma Stone sings “Here’s to the hearts that ache, here’s to the mess we make,” it has a dramatic/musical/spiritual impact equal to that of Liza Minnelli singing the title number of “Cabaret.” It is that gorgeous, that heartbreaking, that uplifting, that amazing. Stone’s performance is timeless — I have never noticed more the way her large almond eyes evoke Charlie Chaplin — and what reverberates right off the screen is the lilt of that melody. It’s a miracle of melancholy perfection.

That’s another reason “La La Land” gets better the second time you see it: You now have those songs in your system. And why should it be otherwise? Great pop songs don’t necessarily hit us with their ultimate force the first time we hear them; often, on the radio, they kick in that second or third or fourth time. In my own second experience with “La La Land,” I felt like I melted, all the more, into the story those melodies were telling. And I do mean melodies (though the lyrics are lovely). What I heard the second time is how Justin Hurwitz constructed the songs out of bits and pieces of the same musical motifs, so that they flow in and out of each other and merge; it’s really a unified song suite. By the end, the music has become a character in the film (which may be why there are so few actual supporting characters). Just watch the scene near the end where Mia is seated in the nightclub and Sebastian, on stage, sits at the piano and plays, very slowly, with one hand, those notes. Da da da da da da…daaa. Those simple seven notes tell the entire story we’ve been watching.

Then there’s the “Whoa, I didn’t expect that!” ending. Instead of a shoot-the-works production number, “La La Land” culminates in a shoot-the-works piece of alternate reality: Call it “That’s Entertainment!” by way of Charlie Kaufman. Mia, in that club, imagines the life that she could have had if she’d remained with a certain person (or is it his fantasy? or both of theirs?) — and the first time I saw the film, it looked, quite simply, like scenes-from-a-road-not-take. But on second viewing, I saw that this rapid-fire home-movie hallucination is something more: It’s the very movie we would have been watching had “La La Land” simply been the delectable old-fashioned musical we think, for an hour or so, it is. The incandescence of “La La Land” is that while it isn’t that movie, it contains that movie, and it leaves us in a bittersweet swoon over the happy endings we long for that can no longer be, because they’ve all been replaced by the beautiful mess we make.